A relief organization supplies blankets, cots, and lanterns to victims of fires, floods, and other natural disasters. One week the organization purchased 10 blankets, 10 cots, and 20 lanterns for a total cost of $1800. The second week, at the same prices, the organization purchased 20 blankets, 20 cots, and 10 lanterns for a total cost of $2400. The third week, at the same prices, the organization purchased 20 blankets, 10 cots, and 10 lanterns for a total cost of $1650. Find the cost of one blanket, the cost of one cot, and the cost of one lantern.
A) $25 per blanket; $76 per cot; $39 per lantern
B) $26 per blanket; $76 per cot; $39 per lantern
C) $25 per blanket; $75 per cot; $40 per lantern
D) $26 per blanket; $75 per cot; $40 per lantern
E) $24 per blanket; $75 per cot; $39 per lantern

Question

Quizplus · Accepted Answer

Let x be the cost of one blanket, y be the cost of one cot, and z be the cost of one lantern. Then we can set up the following system of equations:
10x + 10y + 20z = 1800
20x + 20y + 10z = 2400
20x + 10y + 10z = 1650
Simplifying each equation by dividing by 10, we get:
x + y + 2z = 180
2x + 2y + z = 240
2x + y + z = 165
Solving this system of equations (e.g. by elimination or substitution), we get x = 25, y = 75, and z = 40. Therefore, the cost of one blanket is $25, the cost of one cot is $75, and the cost of one lantern is $40. Therefore, the answer is choice C.

A Relief Organization Supplies Blankets, Cots, and Lanterns to Victims